Question

Two teams A and B play a series ofgames until one team wins four games. Assume that the outcomes of the gamesare independent and that the probability that A wins any one game isp. Whatis the probability that the series lasts five games?

Answer 1

Since we assume the outcome of the games are independent and the probability that A wins any one game is p. We will have that:

The probability that:

Team A wins in 5 games =
`p^(4) (1p)`

Team B wins in 5 games =
`p(1p)^(4)`

Since there are 4 ways each team can win in 5 games, the probability that the series last 5 games is:

`4[p^(4) (1p)+p(1p)^(4) ]`

Thus, the answer is:

`4[p^(4) (1p)+p(1p)^(4) ]`

Answer 2

Explanation:

Please find the answer in this photo below

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